Dynamic response prediction of water medium explosion container based on convolutional neural network

Abstract

The water medium explosion container is an experimental device that simulates explosion in different water depth environments by loading different hydrostatic pressures and different doses of explosive. To ensure its safety during service, it is necessary to study the dynamic response of water medium explosion container. Because the dynamic response is complicated and the correlation between the response and the load of the container is nonlinear, it is difficult to calculate the dynamic response by analytical and numerical methods. In this paper, a model is built based on convolutional neural network (CNN) to predict the dynamic response of water medium explosion container. The accuracy and usability of the CNN prediction model are verified by comparison with the prediction results of the BP neural network model. The results show that CNN can be effectively used to predict the strain response of the dynamic response of water medium explosion container. and this method will play an important role in the later study of the overall feature analysis of the dynamic response of the water medium explosion vessel.

Keywords

Water medium explosion container dynamic response convolutional neural network bp neural network

1. Introduction

The water medium explosion container is an experimental device that simulates explosion in different water depth environments by loading different hydrostatic pressures and different doses of explosive [1, 2]. During service the container will inevitably suffer from damage and performance degradation, so it is necessary to study the dynamic response of water medium explosion container to ensure its safety.

Because the distribution of the load is very complex inside the water medium explosion vessel, it is difficult to analyze the dynamic response by the theoretical method, and the numerical simulation and test methods are main ways at present. Around 2000, Russian scientists Ivanov, Mineev, Zhukov, and Ryzhanskii discovered that the container can be considered to be in a one-way strain state by testing the liquid-filled cylindrical explosive container of metal materials [3, 4, 5, 6, 7]. In addition, Ma et al. numerically simulated the elliptical head cylindrical explosive container under different TNT equivalents. The simulation results showed that the strain of the blast surface was larger than other places and reaches the maximum at the initial stage [8]. Li used the nonlinear finite element method to simulate the action load and dynamic response of the cylindrical explosive container with elliptical head, and the research shows the top load of the head is larger than that of the central section of vessel [9] due to the convergence. Based on the theory of thin-walled shells and the theory of underwater explosion, FAN Zijian deduces the relationship between elastic strain and vessel diameter, wall thickness and dose, and proves that the formula is consistent with the experimental results [10]. Some preliminary laws of dynamic response of water explosion vessel have been obtained. However, the dynamic characteristic of the dynamic response law of the vessel is not be obtained by the numerical simulation method during its service, so the dynamic response prediction by machine learning algorithm becomes an effective method to the dynamic response analysis of the vessel on the basis of the dynamic test data of the vessel

Some scholars have introduced machine learning algorithm into structural dynamic response prediction in recent years. Guo et al. utilized the RBF neural network to precede the dynamic response prediction upon the real time seismic data, some problems are solved such as time lag which exists in the vibration controlling and the noise disturbing of the measure system effectively [11] Wang et al. proposed a novel nonlinear model predictive control method for helicopter/turboshaft engine with variable rotor speed based on neural network [12] Xu et al. applicated back propagation neural network on debonding prediction of glass curtain walls with concealed frames to predict the combined degumming state based on numerical simulation sample [13]. Wang et al. constructed the GRNN model of coal section pillar width prediction in fully mechanized face and it is found that GRNN model has good stability and accuracy for nonlinear coupling prediction results of many influencing factors [14]. My research team has used neural network to predict peak strain of water medium explosion container, and In our previous work, GRNN and BP neural network had been applied to predict the dynamic response of water medium explosion container [15]. But when the number of tests is taken as the input parameter of the model, the predicted results are quite different from the experimental results of vessel under ultimate load, we want to find a prediction algorithm to solve this problem.

Convolution neural network model is mainly used for high-dimensional image classification. Wang et al. identify the gravity anomaly body based on the CNN [16]. Cao et al. proposed a tool condition monitoring approach based on CNN, the approach improved the accuracy and generalization [17]. Zhang et al. proposed an electrocardiogram signal quality assessment method based on convolution neural network, in which the features can be automatically learned by network model [18]. Few people used it for prediction and regression. Sun and Zhou established a surface grinding temperature prediction model based on CNN, and the results showed that the grinding temperature prediction model based on convolutional neural network has strong learning ability and nonlinear fitting ability, which greatly improves the prediction accuracy of grinding temperature [19]. Zhou et al. predict the quality of aerospace assembly holes based on CNN, in which the process parameters and spindle current signal are input to the network, and the burr height of the hole outlet is used as the prediction target [20]. Lu et al. proposed a deep convolutional neural network architecture to estimate local SNR of the seismic data, and synthetic data and real data tests show the effectiveness and efficiency of the method to estimate the SNR and evaluate the quality of seismic data [21]. These results show that CNN is feasible for dynamic response prediction of the water medium explosion vessel.

As for the dynamic response analysis of the water medium explosion vessel, in addition to the peak response prediction, we also hope to obtain the overall characteristics of the time-varying response signal. Therefore, in this paper, CNN is used to predict the peak strain of the water medium explosion vessel, and its feasibility is verified through the comparative analysis with the prediction effect of BP neural network, in order to provide support for feature extraction to the overall response time-varying signal in the later study.

2. Convolutional neural network

Convolutional neural network is an improvement of BP neural network, which is composed of input layer, convolution layer, activation function, pooling layer and full connection layer. and uses the reverse propagation error to adjust and update the weight and bias value of each node connection. Compared with BP neural network, in convolution neural network the connection between the nodes of two adjacent layers is no longer the connection between two nodes, and there are connections only between some nodes. So the number of parameters of the CNN model are greatly reduced. The structure of the convolutional neural network is shown in the Fig. 1.

Figure 1.

Convolutional neural network structure.

2.1 Convolution layer

Convolution layer corresponds to the convolution process in neural network, the input of which may be the input layer data or the data come from pooling layer. The action of convolution filter on all feature spaces of input data, is the data of each sensing area is multiplied by the weight of convolution filter, and then the summation is the input of the next layer of neurons.

2.2 Pooling layer

The pooling layer, also known as the lower sampling layer, is a sampling process to the results of the convolution process. This sampling process can be in the form of selecting the maximum value or the mean value of a given area. Among them, max pool sampling is a non-linear down sampling method, which can reduce the dimension of convoluted results.

2.3 Full connection layer

Convolution neural network usually adds a full connection layer after several convolution and pooling processes. The function of the full connection layer is to ensure that the features of the previous local connections are not lost. It combines the results after convolution and pooling processes, and finally outputs the results. Commonly used activation functions include relu, sigmoid, prelu, tanh, etc.

The training algorithm mainly includes two stages: the forward propagation of information and the reverse propagation of error. Firstly, the data of input layer is transferred to the middle layer, and finally the predicted value is output through the middle volume layer, pool layer and full connection layer. Then by the comparing of the output value with the target value, it begins to enter the stage of error reverse propagation when the error is too large and exceeds a certain threshold value. In the stage of error reverse propagation, the error of the previous layer is calculated by gradient descent based on the error of the output layer, and then the weight is adjusted until the first convolution layer is reached.

3. Data processing

3.1 Data collection and selection of influencing factors

The test was carried out using a cylindrical water medium explosion container capable of simulating a water depth of 200 m with a 10 g TNT equivalent. The water medium explosion test carried out 18 different working conditions under 2 kinds of TNT equivalents (0.8 g, 2.4 g) and 9 kinds of hydrostatic pressure conditions (0, 0.3, 0.5, 0.8, 1, 1.3, 1.5, 1.8, 2 MPa), respectively.

In order to increase the amount of valid data, we arranged three positions on the top and the middle ring of the container head, and each position is set to 15 test points. In the condition of 2.4 g TNT equivalent and 1.5 MPa hydrostatic pressure, we performed two tests due to an accidental situation. In this test, the uncollected data was finally removed, and the actual sample size was 782, as shown in Table 1.

Table 1
Actual sample size for each condition

Dosage (g)	Hydrostatic pressure (MPa)	Sample size
0.8	0	43
	0.3	42
	0.5	43
	0.8	43
	1	42
	1.3	39
	1.5	42
	1.8	43
	2	42
2.4	0	43
	0.3	41
	0.5	43
	0.8	43
	1	41
	1.3	43
	1.5	65
	1.8	43
	2	41

According to the literature reading, it is found that the factors affecting the dynamic response of the water medium explosion vessel are test times, dose, hydrostatic pressure, measuring point position, load, diameter and wall thickness. The feature selection of XGBoost model is used for feature selection to determinate influencing factors related to the dynamic response of the water medium explosion vessel. First, the XGBoost model was constructed, in which these variables were respectively characterized as the 0th, 1st, 2nd, 3rd, 4th, 5th, and 6th input variable. The goodness of fit of the training set without adjustment is 0.7713 and the goodness of fit of the test set is 0.8055. Second, parameter adjustment is performed in the form of grid search. According to the set parameter pool, parameter optimization is performed to obtain the optimal parameter value and the optimal model. After tuning, the goodness of fit of the test set is 0.7773, and the goodness of fit of the training set is: 0.8121. The specific parameters are shown in Table 2.

Table 2

Parameter adjustment

Parameter	Setting range	Optimal parameter
n_estimators	(20,81,10)	20
learning_rate	[0.2,0.1,0.05,0.02,0.01]	0.2
max_depth	[4,6,8]	6
min_samples_leaf	[3,5,9,14]	3
max_features	[3,4]	3

Finally, according to the XGBoost optimal model, the importance of the model features is ranked. The result is shown in Fig. 2. It can be seen from Fig. 2 that the four variables of test number, dose, hydrostatic pressure, and location of the measuring point have a greater influence on the dynamic response of the aqueous medium explosion vessel in this test.

3.2 Treatment of abnormal value

The dynamic response data of the water medium explosion container is generated by actual measurement, so the data always have varieties of noise jamming. If the data is directly used to train the model, the prediction effect of the model is not satisfactory. Therefore, we detected outliers and analyzed the data by means of isolated forests, local outlier detection and box plots. The results are shown in Table 3.

Table 3
Comparison of abnormal value measurements

Sample	Size	Mean	Max	Min	Std
Raw data	782	88.34	1067.4	12.13	81.40
Remove outliers by Isolated Forest	742	76.60	192.56	12.13	36.55
Remove outliers by Box Plot	748	77.74	210.78	12.13	38.14
Remove outliers by Local Outlier	744	77.98	181.98	19.12	36.77

Figure 2.

XGBoost feature importance.

As can be seen from the Table 3, the 40 outliers were eliminated by detecting of the isolated forest algorithm, and the standard deviation decreased from the original 81.4 to 36.55, with a drop of 55.10%. The 34 data were eliminated by outlier detection of box plot, the standard deviation decreased from 81.4 to 38.14, with a decrease of 53.14%. By detecting the local outliers and eliminating 38 data, the standard deviation decreased from the original 81.4 to 36.77, with a decrease of 54.83%. According to the outlier detection of this test data, isolated forests have the best effect in the detection of outliers, followed by local outliers, and box plots are slightly inferior to the other two, and box plot and local outlier can only handle the abnormal value of a single variable. Therefore, the outlier detection in this study uses an isolated forest treatment method.

3.3 Smoothing processing and normalization

During the experiment, due to the influence of the test instrument and external conditions, the maximum strain value collected has noise interference. In order to better fit the model, we smooth the data moving average filter with a window of 15. The effect of data smoothing is shown in Fig. 3.

For eliminating the dimensional relationship between variables, the data is normalized to make the data comparable by the Standard Scaler function of Python software.

Figure 3.

Data smoothing.

4. Dynamic response prediction

4.1 Prediction model

In this paper, the dynamic response prediction models are built based on CNN and BP respectively, the input variables of which are test times T, test point location L, charge Q and hydrostatic pressure P, and the output variable of which is the maximum strain s.

4.1.1 Convolutional neural network regression model

The input layer of convolution neural network regression model has 4 dimensions, which constitutes 2*2 matrix. The input variables are the number of experiments, the location of measuring points, the dosage and the hydrostatic pressure. The output variable is the maximum strain. The model takes 6/7 of the sample as training data and 1/7 of the sample as test data. After 2000 training, the error was reduced to 0.20. The effect of simulation is shown in Fig. 4.

Figure 4.

Simulation effect of CNN.

4.1.2 BP neural network model

BP neural network model adopts three-layer network structure. The number of nodes in the input layer is 4, the number of nodes in the hidden layer is determined to 30 by trial and error method and the number of nodes in the output layer is 1. The parameters of BP neural network model are optimized by genetic algorithm. After 10000 iterations, the optimal individual is found, that is, the optimal initial threshold and weight of the optimal BP neural network. The effect of simulation is shown in Fig. 5.

4.2 Error analysis

Three indexes are adopted to evaluate the prediction effect of different models, which are mean absolute error (MAE), mean absolute percentage error (MAPE) and fitness ( $R^{2}$ ) respectively. They are defined as follows:

$\displaystyle\text{MAE}=\frac{\sum\limits_{i=1}^{N}{\left|\hat{y}_{i}-y_{i}% \right|}}{N}$ (1) $\displaystyle\text{MAPE}=\frac{\sum\limits_{i=1}^{N}{\left|{\frac{\hat{y}_{i}-% y_{i}}{y_{i}}}\right|}}{N}$ (2) $\displaystyle R^{2}=\frac{\text{SSR}}{\text{SST}}=\frac{\sum\limits_{i=1}^{N}{% \left(\hat{y}_{i}-\bar{y}\right)^{2}}}{\sum\limits_{i=1}^{N}{\left({y_{i}-\bar% {y}}\right)^{2}}}$ (3)

Where, $\widehat{y_{i}}$ is the predicted value, $y_{i}$ is the true value, $\bar{y}$ is the arithmetic mean.

First, a comparative analysis was performed to the training set. It can be seen from Table 3 that the goodness of fit of the CNN model is bigger than that of the BP neural network model, and the value of MAPE of the CNN model are smaller than that of the BP neural network model. Therefore, from the training set, the convolutional neural network has a good fitting effect on the training set.

Table 4

Comparison of test errors of three models

Models	R ${}^{2}$ (training set)	R ${}^{2}$ (testing set)	MAE (training set)	MAE (testing set)	MAPE (training set)	MAPE (testing set)
CNN	0.8152	0.7547	8.65	6.74	9.35	11.41
BP	0.8041	0.8240	7.08	6.76	9.72	9.21

Figure 5.

BP neural network regression prediction.

Second, a comparative analysis was performed to the testing set. It is known from Table 3 that the goodness of fit of the CNN model is smaller than that of the BP neural network model, and the value of MAPE of the CNN model are bigger than that of the BP neural network model. Therefore, to the testing set, the predict effect of convolutional neural network is slightly less than BP neural network model.

In summary, the convolutional neural network is an effective method to predict the dynamic response of water medium explosion container, and the simulation results show the validity and accuracy of the model.

4.3 Analysis of prediction results under the limit load

The dynamic response prediction of water explosion vessel provides the basis for the reliability analysis of the vessel. The reliability analysis usually considers the comparison of the strength and stress of the vessel under the limit load, so it is necessary to use the prediction model to predict the response of the vessel under the limit state. Therefore, the prediction effect of the prediction model is not only measured by the average prediction error of the model, but also measured by the prediction accuracy to the dynamic response of the container under the limit load. In this paper, CNN prediction model and BP neural network model are respectively used to predict the response of the container under the limit load, and compared with the test data of the container. The comparison data is shown in Table 5.

Table 5
Comparison of predict results under the limit load

Models	Strain/ $\mu\varepsilon$	Prediction absolute error	Prediction relative error
Measured	585	0	0
CNN	542	43	7%
BP	416	169	29%

It can be seen that compared with BP model, CNN model has a higher accuracy in response prediction of vessel under limit load. The main reason is that most of the load in the sample data deviates from the limit load far, so the model training is greatly affected by the number of tests. The CNN model has better prediction effect because of its strong feature analysis ability and constant correction of its weight proportion.

5. Conclusions

(1)

In this paper, a convolution neural network model is proposed to predict the dynamic response of water explosion vessel. The dynamic response test data is pre-processed to obtain better forecasting effect. Through comparison, it is found that the prediction effect of the prediction model in the test data is basically the same as that of BP neural network, which has a high prediction accuracy.

(2)

In this paper, CNN prediction model and BP neural network model are respectively used to predict the response of the container under the limit load, and compared with the test data of the container. Compared with BP model, CNN model has a higher accuracy in response prediction of vessel under limit load by feature recognition, then the prediction results can be taken as the premise of the reliability analysis of the vessel.

(3)

This prediction only considers the peak response of the vessel, and does not analysis the time-varying signal of the overall response. Therefore, it does not give full play to the advantages of convolution neural network in the feature extraction of high-dimensional data. It can be predicted that this method will play an important role in the later study of the overall feature analysis of the dynamic response of the water medium explosion vessel.

Footnotes

Acknowledgments

This work was support by NSFC51404175 and the Hubei Province Key Laboratory of Systems Science in Metallurgical Process Foundation under Grant No. Y201712.

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Dynamic response prediction of water medium explosion container based on convolutional neural network

Abstract

Keywords

1. Introduction

2. Convolutional neural network

2.2 Pooling layer

2.3 Full connection layer

3. Data processing

3.1 Data collection and selection of influencing factors

Table 1 Actual sample size for each condition

Table 3 Comparison of abnormal value measurements

4.1 Prediction model

4.1.1 Convolutional neural network regression model

4.2 Error analysis

Table 5 Comparison of predict results under the limit load

Footnotes

Acknowledgments

References

Table 1
Actual sample size for each condition

Table 3
Comparison of abnormal value measurements

Table 5
Comparison of predict results under the limit load